Did God intend to save all humanity? - Yes
Does God intend to save all humanity? - Yes
Will God save all humanity? - Yes
1 Tim 2:4,6 - 4Who will have all men to be saved, and to come unto the knowledge of the truth.
6Who gave himself a ransom for all, to be testified in due time.
1 John 4:14 - 14And we have seen and do testify that the Father sent the Son to be the Saviour of the world.
John 12:32 - 32And I, if I be lifted up from the earth, will draw all men unto me.
Hebrews 7:25 - 25Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.
Romans 11:26 - 26And so all Israel shall be saved: as it is written, There shall come out of Sion the Deliverer, and shall turn away ungodliness from Jacob:
Acts 3:20-21 20And he shall send Jesus Christ, which before was preached unto you:
21Whom the heaven must receive until the times of restitution of all things, which God hath spoken by the mouth of all his holy prophets since the world began.
Just to name a scant few verses.